Diversity calculation
Masatoshi Katabuchi
2021/11/9
Course materials for 2020-11-2 AFEC at XTBG.
1 Prerequisites
Did you install picante and FD?
install.packages("picante")
install.packages("FD")It’s better if you have those packages too.
install.packages("tidyverse")
install.packages("rmarkdown")
install.packages("DT")Load pacakges.
library(picante)
library(FD)
library(tidyverse)
library(rmarkdown)2 Data
2.1 Community
samp <- read_csv("./data/samp.csv")
DT::datatable(samp)samp_mat <- as.matrix(samp[, -1])
rownames(samp_mat) <- samp$Site
samp_mat## Illicium_macranthum Manglietia_insignis Michelia_floribunda Beilschmiedia_robusta Neolitsea_chuii Lindera_thomsonii Actinodaphne_forrestii
## Site1 1 0 0 0 0 0 0
## Site2 1 2 2 2 0 0 0
## Site3 1 0 0 0 0 2 2
## Site4 1 1 0 0 0 2 2
## Site5 1 0 0 0 1 1 0
## Machilus_yunnanensis
## Site1 0
## Site2 0
## Site3 2
## Site4 0
## Site5 02.2 Phylogeny
phylo <- read.tree("./data/dummy_tree.newick")
plot(phylo)
2.3 Traits
| Abbreviation | Trait | Unit |
|---|---|---|
| LMA | Leaf mass per area | g m-2 |
| LL | Leaf lifespans (longevity) | months |
| Amass | Maximum photosynthetic rates per unit mass | nnoml g-1 s-1 |
| Rmass | Dark resperation rates per unit mass | nnoml g-1 s-1 |
| Nmass | Leaf nitrogen per unit mass | % |
| Pmass | Leaf phosphorus per unit mass | % |
| WD | Wood density | g cm-3 |
| SM | Seed dry mass | mg |
trait <- read_csv("./data/dummy_trait.csv")
# trait <- read.csv("./data/dummy_trait.csv") is fine too.
DT::datatable(trait)2.4 Check the histograms of trait values first
trait_long <- trait %>%
gather(trait, val, 2:9)
ggplot(trait_long, aes(x = val)) +
geom_histogram(position = "identity") +
facet_wrap(~ trait, scale = "free")
Probably we can do log-transformation for all the traits except for WD.
trait2 <- trait %>%
mutate(logLMA = log(LMA),
logLL = log(LL),
logAmass = log(Amass),
logRmass = log(Rmass),
logNmass = log(Nmass),
logPmass = log(Pmass),
logSM = log(SM)) %>%
dplyr::select(sp, logLMA, logLL, logAmass, logRmass, logNmass, logPmass, WD, logSM)
DT::datatable(trait2)trait2 %>%
gather(trait, val, 2:9) %>%
ggplot(., aes(x = val)) +
geom_histogram(position = "identity") +
facet_wrap(~ trait, scale = "free")
3 Fisrt-order metrics (without phylogeny or traits)
3.1 Species richness, Beta diversity metrics
Skip
3.2 Nonmetric Multidimensional Scaling (NMDS)
res_mds <- metaMDS(samp_mat)## Run 0 stress 0
## Run 1 stress 0
## ... Procrustes: rmse 0.0494734 max resid 0.07992025
## Run 2 stress 0
## ... Procrustes: rmse 0.0556183 max resid 0.07171984
## Run 3 stress 0
## ... Procrustes: rmse 0.1318025 max resid 0.2376398
## Run 4 stress 0.09680968
## Run 5 stress 0.1302441
## Run 6 stress 0.09681
## Run 7 stress 0.1302441
## Run 8 stress 7.519671e-05
## ... Procrustes: rmse 0.1287863 max resid 0.1984166
## Run 9 stress 0
## ... Procrustes: rmse 0.1015581 max resid 0.1639114
## Run 10 stress 0
## ... Procrustes: rmse 0.1239007 max resid 0.1920471
## Run 11 stress 8.083837e-05
## ... Procrustes: rmse 0.1288717 max resid 0.198636
## Run 12 stress 8.883421e-05
## ... Procrustes: rmse 0.12886 max resid 0.1986286
## Run 13 stress 0
## ... Procrustes: rmse 0.1190997 max resid 0.2045357
## Run 14 stress 0
## ... Procrustes: rmse 0.04819579 max resid 0.08233104
## Run 15 stress 0
## ... Procrustes: rmse 0.04568752 max resid 0.07367699
## Run 16 stress 0.2297529
## Run 17 stress 0.1302441
## Run 18 stress 0
## ... Procrustes: rmse 0.1100394 max resid 0.15909
## Run 19 stress 0.1302441
## Run 20 stress 0.09681026
## *** No convergence -- monoMDS stopping criteria:
## 12: stress < smin
## 2: stress ratio > sratmax
## 6: scale factor of the gradient < sfgrminplot(res_mds)
We can use the function ordiplot and orditorp to add text to the plot in place of points to make some more sence.
ordiplot(res_mds, type = "n")
orditorp(res_mds,display="species",col="red",air=0.01)
orditorp(res_mds,display="sites",cex=1.25,air=0.01)
4 Phylogenetic metrics
4.1 Branch length based metric
4.1.1 PD
res_pd <- pd(samp_mat, phylo)
res_pd## PD SR
## Site1 1.000000 1
## Site2 3.022727 4
## Site3 2.909091 4
## Site4 3.136364 4
## Site5 2.454545 3You can always see the help.
?pd4.2 Distance based metric
cophenetic() creates distance matrices based on phylogenetic trees. Let’s see the first 5 species.
cophenetic(phylo)[1:5, 1:5]## Acer_campbellii Melia_toosendan Skimmia_arborescens Rhus_sylvestris Sterculia_nobilis
## Acer_campbellii 0.0000000 0.18181818 0.18181818 0.3636364 0.5454545
## Melia_toosendan 0.1818182 0.00000000 0.09090909 0.3636364 0.5454545
## Skimmia_arborescens 0.1818182 0.09090909 0.00000000 0.3636364 0.5454545
## Rhus_sylvestris 0.3636364 0.36363636 0.36363636 0.0000000 0.5454545
## Sterculia_nobilis 0.5454545 0.54545455 0.54545455 0.5454545 0.00000004.2.1 MPD
\(MPD = \frac{1}{n} \Sigma^n_i \Sigma^n_j \delta_{i,j} \; i \neq j\), where \(\delta_{i, j}\) is the pairwised distance between species i and j
res_mpd <- mpd(samp_mat, cophenetic(phylo))
res_mpd## [1] NA 1.568182 1.454545 1.606061 1.636364The above vector shows MPD for each site.
4.2.2 MNTD
\(MNTD = \frac{1}{n} \Sigma^n_i min \delta_{i,j} \; i \neq j\), where \(min \delta_{i, j}\) is the minimum distance between species i and all other species in the community.
res_mntd <- mntd(samp_mat, cophenetic(phylo))
res_mntd## [1] NA 1.181818 1.181818 1.295455 1.2727275 Functional metrics
5.1 Community weighted means (CWM)
\[ CWM_i = \frac{\sum_{j=1}^n a_{ij} \times t_{j}}{\sum_{j=1}^n a_{ij}} \]
tmp <- trait2 %>%
filter(sp %in% colnames(samp_mat))
tmp## # A tibble: 8 × 9
## sp logLMA logLL logAmass logRmass logNmass logPmass WD logSM
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Actinodaphne_forrestii 4.24 2.53 5.01 2.17 0.412 -1.83 0.48 0.300
## 2 Beilschmiedia_robusta 3.61 3.09 5.72 3.53 1.75 -1.35 0.47 0.770
## 3 Illicium_macranthum 5.66 4.75 3.27 0.793 -0.288 -3.51 0.4 -0.0305
## 4 Lindera_thomsonii 4.47 3.70 5.49 3.02 0.626 -3.00 0.53 -0.734
## 5 Machilus_yunnanensis 4.26 3.36 4.65 2.69 0.239 -0.821 0.59 0.0770
## 6 Manglietia_insignis 6.22 5.24 3.10 0.255 -0.431 -3.91 0.45 -0.0513
## 7 Michelia_floribunda 4.93 3.99 3.65 2.00 0.457 -3.91 0.54 0.621
## 8 Neolitsea_chuii 4.65 4.18 5.20 2.30 0.489 -2.12 0.43 -1.71(ab <- apply(samp_mat, 1, sum))## Site1 Site2 Site3 Site4 Site5
## 1 7 7 6 3# inner product
(CWS <- samp_mat %*% as.matrix(tmp[,-1]))## logLMA logLL logAmass logRmass logNmass logPmass WD logSM
## Site1 4.236712 2.527327 5.006359 2.173615 0.4121097 -1.832581 0.48 0.3001046
## Site2 31.729450 25.585161 33.973907 16.848875 4.5974297 -17.531309 3.28 0.3114643
## Site3 35.828159 29.342331 28.910240 11.266140 1.4425535 -21.721201 3.32 -1.9909259
## Site4 30.140733 24.069613 24.233478 10.201674 2.2197972 -18.827747 2.93 2.2087792
## Site5 14.713415 11.128090 12.759265 5.116104 0.2203436 -6.565585 1.52 0.3257723(CWM <- CWS / ab)## logLMA logLL logAmass logRmass logNmass logPmass WD logSM
## Site1 4.236712 2.527327 5.006359 2.173615 0.41210965 -1.832581 0.4800000 0.3001046
## Site2 4.532779 3.655023 4.853415 2.406982 0.65677568 -2.504473 0.4685714 0.0444949
## Site3 5.118308 4.191762 4.130034 1.609449 0.20607908 -3.103029 0.4742857 -0.2844180
## Site4 5.023456 4.011602 4.038913 1.700279 0.36996620 -3.137958 0.4883333 0.3681299
## Site5 4.904472 3.709363 4.253088 1.705368 0.07344788 -2.188528 0.5066667 0.10859085.2 Distance based metrics
5.2.1 Prepare a trait distance matrix
We have a data.fame of traits. First we need to prepare a trait matrix, then a distance matrix based on trait values.
trait_mat0 <- as.matrix(trait2[, -1])
rownames(trait_mat0) <- trait2$spLet’s see a subset of the trait matrix
trait_mat0[1:5, 1:5]## logLMA logLL logAmass logRmass logNmass
## Acer_campbellii 3.684118 1.957274 6.892692 4.002047 1.8809906
## Actinodaphne_forrestii 4.236712 2.527327 5.006359 2.173615 0.4121097
## Alnus_nepalensis 4.743366 4.010419 4.341335 2.022871 0.5007753
## Anneslea_fragrans 4.190715 3.293241 5.162211 3.703522 1.4632554
## Beilschmiedia_robusta 3.614964 3.085573 5.722441 3.526655 1.7544037Then, we will make trait distance matrix based on the Euclidean distance. There are other distance measures, for example Gower’s Distance, but we focus on the Euclidean distance today.
Before calulating distance, we need to make sure unit change in ditances have same for different traits. We will scale trait values so that then have mean = 0 and SD = 1. (e.g., \((X_i - \mu) / \sigma\))
trait_mat <- scale(trait_mat0)
par(mfrow = c(2, 2))
hist(trait_mat0[, "logLMA"])
hist(trait_mat[, "logLMA"])
hist(trait_mat0[, "WD"])
hist(trait_mat[, "WD"])
par(mfrow = c(1, 1))Now we can make a trait distance matirx.
trait_dm <- as.matrix(dist(trait_mat))Let’s see the first 5 species.
trait_dm[1:5, 1:5]## Acer_campbellii Actinodaphne_forrestii Alnus_nepalensis Anneslea_fragrans Beilschmiedia_robusta
## Acer_campbellii 0.000000 3.799360 5.216902 3.175911 2.545269
## Actinodaphne_forrestii 3.799360 0.000000 2.415031 2.335392 2.565063
## Alnus_nepalensis 5.216902 2.415031 0.000000 3.225141 3.638183
## Anneslea_fragrans 3.175911 2.335392 3.225141 0.000000 1.579930
## Beilschmiedia_robusta 2.545269 2.565063 3.638183 1.579930 0.0000005.2.2 MPD
mpd(samp_mat, trait_dm)## [1] NA 4.288349 3.530805 3.961248 3.438008ses.mpd(samp_mat, trait_dm)## ntaxa mpd.obs mpd.rand.mean mpd.rand.sd mpd.obs.rank mpd.obs.z mpd.obs.p runs
## Site1 1 NA NaN NA NA NA NA 999
## Site2 4 4.288349 3.691006 0.7998219 778 0.7468451 0.778 999
## Site3 4 3.530805 3.716439 0.8330723 449 -0.2228307 0.449 999
## Site4 4 3.961248 3.716864 0.8207042 651 0.2977734 0.651 999
## Site5 3 3.438008 3.734081 0.9908050 435 -0.2988209 0.435 9995.2.3 MNTD
mntd(samp_mat, trait_dm)## [1] NA 2.504352 2.697074 1.873825 2.6135855.3 Branch length based metric
5.3.1 FD
We will make a functional dendrogram using clustring methods. We use UPGMA in this example.
t_clust <- hclust(dist(trait_mat), method = "average")
plot(t_clust)
5.3.2 More functional diversity metrics
res_fd <- dbFD(trait_mat[colnames(samp_mat), ], samp_mat)## FEVe: Could not be calculated for communities with <3 functionally singular species.
## FDis: Equals 0 in communities with only one functionally singular species.
## FRic: To respect s > t, FRic could not be calculated for communities with <3 functionally singular species.
## FRic: Dimensionality reduction was required. The last 5 PCoA axes (out of 7 in total) were removed.
## FRic: Quality of the reduced-space representation = 0.811349
## FDiv: Could not be calculated for communities with <3 functionally singular species.res_fd## $nbsp
## Site1 Site2 Site3 Site4 Site5
## 1 4 4 4 3
##
## $sing.sp
## Site1 Site2 Site3 Site4 Site5
## 1 4 4 4 3
##
## $FRic
## Site1 Site2 Site3 Site4 Site5
## NA 5.453089 2.917904 3.000656 3.553247
##
## $qual.FRic
## [1] 0.811349
##
## $FEve
## Site1 Site2 Site3 Site4 Site5
## NA 0.7595456 0.6769400 0.7085376 0.7584941
##
## $FDiv
## Site1 Site2 Site3 Site4 Site5
## NA 0.7301943 0.7617251 0.9166699 0.8261683
##
## $FDis
## Site1 Site2 Site3 Site4 Site5
## 0.000000 2.710994 1.842262 2.311159 2.042416
##
## $RaoQ
## Site1 Site2 Site3 Site4 Site5
## 0.000000 8.376023 4.005094 5.664467 4.379844
##
## $CWM
## logLMA logLL logAmass logRmass logNmass logPmass WD logSM
## Site1 1.4467783 1.17548950 -1.38976382 -1.9975087 -0.88119735 -1.2775781 -1.0150179 -0.2191496
## Site2 0.5666449 0.55085046 -0.56218769 -0.8908026 -0.09004842 -0.8660119 -0.2744691 0.1665816
## Site3 -0.1410729 -0.33319385 0.27087040 -0.2062427 -0.24084641 0.2088166 0.1242879 -0.2907346
## Site4 0.3670613 0.03104745 0.01551229 -0.7298853 -0.34295985 -0.5718506 -0.2341187 -0.3397288
## Site5 0.4305791 0.56352114 0.11718014 -0.5812855 -0.29128834 -0.6020974 -0.4833418 -0.97019977 Computing Environment
devtools::session_info()## ─ Session info ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
## setting value
## version R version 4.1.2 (2021-11-01)
## os macOS Big Sur 11.6
## system aarch64, darwin20.6.0
## ui unknown
## language (EN)
## collate en_US.UTF-8
## ctype en_US.UTF-8
## tz Asia/Shanghai
## date 2021-11-05
##
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